# Painting with Diophantine Equations

Solutions of the Diophantine equations xl + ym = zn have been used for the generation of these pictures. The solutions in the x-y plane can be found as black dots in the pictures. Functions fi(x,y) are assigned to each dot i and combined together. They are forming mountains, to which colorful contour lines have been assigned.

## Formula

- x^2 + y = z^2

## Diophantos No 1

-100 < x < 100

-100 < y < 100

Trivial solutions with x=0 or y=0 have been excluded.

## Formula

- x^2 + y^2 = z^2

## Diophantos No 2

Pythagorean triples

-100 < x < 100

-100 < y < 100

Trivial solutions with x=0 or y=0 have been excluded.

## Formula

- x^2 + y^2 = z^2

## Diophantos No 3

Pythagorean triples

-100 < x < 100

-100 < y < 100

Trivial solutions with x=0 or y=0 have been excluded.

## Formula

- x^2 + y^2 = z^3

## Diophantos No 4

-100 < x < 100

-100 < y < 100

Trivial solutions with x=0 or y=0 have been excluded.

## Formula

- x^2 + y^2 = z^4

## Diophantos No 5

-50 < x < 50

-50 < y < 50

Trivial solutions with x=0 or y=0 have been excluded.

## Formula

- x^2 + y^2 = z^4

## Diophantos No 6

-100 < x < 100

-100 < y < 100

Trivial solutions with x=0 or y=0 have been excluded.

## Formula

- x^2 + y^2 = z^4

## Diophantos No 7

-100 < x < 100

-100 < y < 100

Trivial solutions with x=0 or y=0 have been excluded.

## Formula

- x^2 + y^2 = z^4

## Diophantos No 8

-150 < x < 150

-150 < y < 150

Trivial solutions with x=0 or y=0 have been excluded.

## Formula

- x^2 + y^2 = z^4

## Diophantos No 9

-200 < x < 200

-200 < y < 200

Trivial solutions with x=0 or y=0 have been excluded.

## Formula

- x^2 + y^2 = z^4

## Diophantos No 10

-200 < x < 200

-200 < y < 200

Trivial solutions with x=0 or y=0 have been excluded.

## Formula

- x^2 + y^2 = z^4

## Diophantos No 11

-200 < x < 200

-200 < y < 200

Trivial solutions with x=0 or y=0 have been excluded.

## Formula

- x^2 + y^3 = z^2

## Diophantos No 12

-100 < x < 100

-100 < y < 100

Trivial solutions with x=0 or y=0 have been excluded.

## Formula

- x^3 + y = z^2

## Formula

- x^3 + y^3 = z^2

## Formula

- x^3 + y^3 = z^2

## Formula

- x^4 + y^2 = z^2

## Diophantos No 16

-100 < x < 100

-100 < y < 100

Trivial solutions with x=0 or y=0 have been excluded.

## Formula

- x^4 + y^2 = z^2

## Diophantos No 17

-100 < x < 100

-100 < y < 100

Trivial solutions with x=0 or y=0 have been excluded.

## Formula

- x^4 + y^3 = z^2

## Diophantos No 18

-100 < x < 100

-100 < y < 100

Trivial solutions with x=0 or y=0 have been excluded.

## Formula

- x^4 + y^4 = z^3

## Diophantos No 19

-500 < x < 500

-500 < y < 500

Trivial solutions with x=0 or y=0 have been excluded.

## Formula

- x^4 + y^4 = z^3

## Diophantos No 20

-500 < x < 500

-500 < y < 500

Trivial solutions with x=0 or y=0 have been excluded.

## Formula

- x^6 + y^4 = z^2

## Diophantos No 21

-100 < x < 100

-100 < y < 100

Trivial solutions with x=0 or y=0 have been excluded.

## Formula

- x^6 + y^4 = z^2

## Diophantos No 22

-100 < x < 100

-100 < y < 100

Trivial solutions with x=0 or y=0 have been excluded.